Nonlinear susceptibilities of a weakly-disordered uniaxial ferromagnet in the critical region

For the three-dimensional random Ising model, the effective sextic coupling constant v_6 and the nonlinear susceptibilities of the fourth (chi_4) and sixth (chi_6) orders are calculated at criticality. These quantities are shown to differ markedly from their counterparts for pure uniaxial magnets. In particular, the ratio v_6/v_{4}^2 entering the equation of state of the random Ising model turns out to be equal to 0.87, while in pure magnets v_6/v_{4}^2 = 1.65. The universal susceptibility ratios m^3 chi_4/chi^2 and m^6 chi_6/chi^3 (m - the inverse correlation length) are found to differ by factors 1.6 and 2.7, respectively, for random and uniform Ising models. These big differences of the universal quantities can be measured both in physical and computer experiments, and such measurements may be considered as a tool for an identification of the random critical behavior.